Ch. 1 Review

Axioms

100

What is the axiom that states that x + y = y + x and xy = yx

Commutativity of Addition and Multiplication

200

Which axiom states that x = x?

Reflexive Property

300

Which axiom states that x + 0 = x and x(1) = x

Identity of addition and multiplication

400

Which axiom states that if x = 5 and x = y, therefore 

y = 5

Transitivity

500

Which axiom states that if x = y then y = x

Symmetry

Numbers

100

What is the multiplicative inverse of 2/3?

3/2

200

square root of 2

irrational but not transcendental

300

Write an example of an imaginary number

square root of a negative number

400

What is the additive inverse of -7

7

500

Give an example of a positive rational number that is not an integer

any positive fraction

Polynomials

100

9xyz + 2

cubic binomial

200

(3^2xy^3)/z

not a polynomial - division by a variable

300

3x² + 5x - 7

quadratic trinomial

400

6³x⁵y² - 3y⁶

7th degree binomial

500

0x⁵

Monomial with no degree

Equations

100

4x - 6 = 10 {real numbers}

{4}

200

x² = 16 {negative numbers}

{-4} (4)

300

7x - 4 = 2x - 19 {integers}

{-3}

400

(2x - 5)(x + 1) = 0  {real numbers}

{-1, 5/2}

500

x(5x - 3)(x - 6) = 0 {integers}

{0, 6} (3/5)

Inequalities

100

solve and graph the solution set 

5 - 3x > -4 {real numbers}

x < 3

200

solve and graph the solution set

l x l < 5

-5 < x < 5

300

3 < x + 4 < 5

-1 < x < 1

400

l x + 3 l > -6

3 > x > -9

500

Transform the equation x = 5 by multiplying both sides by (x - 2). What is the solution to the transformed equation? What is the solution of the transformed equation called?

{5, 2} 2 is an extraneous solution